After dimension reduction, a deep learning network module is utilized to estimate the transformed device state matrix \(\mathbf {S}\) . In general, the estimator is designed based on the distribution of the device state matrix. Even with dimension reduction, \(\mathbf {S}\)  has the same distribution parameters as \(\mathbf {X}\) . Commonly, \(\mathbf {X}\)  is assumed to be Bernoulli-Gaussian distributed if the channels experience Rayleigh fading [1]}. However, in practical environments, the channels may have an irregular distribution. To enhance the robustness of the estimator, we model \(\mathbf {X}\)  as a Bernoulli-Gaussian mixture distributed random matrix [2]}. With the prior knowledge information, we design a feature-aided adaptive-tuning deep learning (FAT-DL) algorithm based on the architecture of the VAMP algorithm for the design of the estimator in Section IV.
